In this dissertation, we investigate various aspects of signed graphs, with a particular focus on signings and sign-symmetric signed graphs. We begin by examining the complete graph on six vertices with one edge deleted ($K_6$\textbackslash e) and explore the different ways of signing this graph up to switching isomorphism. We determine the frustration index (number) of these signings and investigate the existence of sign-symmetric signed graphs. We then extend our study to the $K_6$\textbackslash 2e graph and the McGee graph with exactly two negative edges. We investigate the distinct ways of signing these graphs up to switching isomorphism and demonstrate the absence of sign-symmetric signed graphs in some cases. We then introduce and study the signed graph class $\mathcal{S}$, which includes all sign-symmetric signed graphs, we prove several theorems and lemmas as well as discuss the class of tangled sign-symmetric signed graphs. Also, we study the graph class $\mathcal{G}$, consisting of graphs with at least one sign-symmetric signed graph, prove additional theorems and lemmas, and determine certain families within $\mathcal{G}$. Our results have practical applications in various fields such as social psychology and computer science.

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This dissertation focuses on studying various network formation games in Economics. We explore a different model in each chapter to capture various aspects of networks. Chapter 1provides an overview of this dissertation. Chapter 2 studies the possible Nash equilibrium configurations in a model of signed network formation as proposed by Hiller (2017). We specify the Nash equilibria in the case of heterogeneous agents. We find 3 possible Nash equilibrium configurations: Utopia network, positive assortative matching, and disassortative matching. We derive the specific conditions under which they arise in a Nash equilibrium. In Chapter 3, we study a generalized model of signed network formation game where the players can choose not only positive and negative links but also neutral links. We check whether the results of the signed network formation model in the literature still hold in our generalized framework using the notion of pairwise Nash equilibrium. Chapter 4 studies inequality in a weighted network formation model using the notion of Nash equilibrium. As a factor of inequality, there are two types of players: Rich players and poor players. We show that both rich and poor players designate other rich players as their best friends. As a result, We present that nested split graphs are drawn from survey data because researchers tend to ask respondents to list only a few friends. / Doctor of Philosophy / This dissertation focuses on studying various network formation games in Economics. We explore a different model in each chapter to capture various aspects of networks. Chapter 1 provides an overview of this dissertation. Chapter 2 studies the possible singed network configurations in equilibrium. In the signed network, players can choose a positive (+) relationship or a negative (-) relationship toward each other player. We study the case that the players are heterogeneous. We find 3 possible categories of networks in equilibrium: Utopia network, positive assortative matching, and disassortative matching. We derive the specific conditions under which they arise in equilibrium. In Chapter 3, we study a generalized model of signed network formation game where the players can choose not only positive and negative links but also neutral links. We check whether the results of the signed network formation model in the literature still hold in our generalized framework. Chapter 4 studies inequality in a weighted network formation model using the notion of Nash equilibrium. In this weighted network model, each player can choose the level of relationship. As a factor of inequality, there are two types of players: rich players and poor players. We show that both rich and poor players choose other rich players as their best friends. As a result, we present that nested split graphs are drawn from survey data because these social network data are censored due to the limit of the number of responses.

Signed language interpreting in South Africa has not received much academic attention, despite the profession having undergone major transformation since the advent of democracy. This study aims to create a better understanding of signed language interpreters’ behaviour in one specific setting in South Africa – post-secondary education. During the researcher’s own practice as an educational interpreter at a post-secondary institution, she experienced role conflict and found little information available to assist her in making professional decisions on which direction to take. This provided the impetus to embark on this research. The study begins by outlining the field of liaison interpreting and educational interpreting, and examining the existing literature regarding the interpreter’s role and norms in interpreting. It then goes on to examine authentic interpreted texts, filmed in actual lectures in post-secondary settings. These texts are analysed with reference to interpreter shifts and deviations from the source text, with particular focus on interpreter-generated utterances (additions), borrowing (fingerspelling), omissions (both errors and conscious choice) and various types of collaboration between the interpreter and primary participants. These shifts are examined in more detail to explore whether they indicate any change in the interpreter’s role. Further, interpreters’ own views about their practice, elicited from individual interviews, enable the reader to understand how the interpreters view the role(s) that they fulfil. The research will provide information for interpreter trainers about the roles assumed by SASL interpreters in higher education and provide a platform from which to scaffold future educational interpreter research and training. / Linguistics / M.A. (Linguistics)

本論文探討的主題有四：（一）陳述中文文法手語與台灣自然手語各語言層級結構的異同，並探查兩套手語系統結構差異部分的語言溝通效率與語意清晰度；（二）瞭解受試者兩套手語系統的語言能力及其語言使用情形；（三）調取受試者對兩套手語系統的語言刻板印象與手語政策態度；（四）探討現階段手語政策的實施。 本論文包含量化與質化的研究方法，研究對象為年滿十八歲、居住在大台北地區、且以手語為主要使用語言之聽覺障礙者。量化研究包含手語結構評估問卷及手語使用情形與語言態度問卷。受試者須先完成結構評估測驗，才進行手語使用情形與語言態度問卷之填答。手語結構評估問卷針對兩套手語系統之迅速程度、模糊程度、與歧異程度加以測試。語言結構評估項目共有基本詞彙、詞組、時貌、副詞、簡單句型、複句句型、與篇章等七大類共一百九十四項，以影片方式呈現。受試者每觀看完一項評估項目，即立刻根據影片內容回答問卷上之題目。語言使用情形與語言態度問卷則探查受試者手語能力、手語使用、及語言態度。本論文以非機率抽樣的滾雪球抽樣方式進行量化問卷的發放，共回收75份有效樣本，進行無母數統計分析。質化研究以深入訪談方式進行，以立意抽樣方式共訪問六名受訪者，重點在探查量化問卷所發現的結果之原因。 研究結果顯示，在結構評估測驗中，除了詞組與簡單句型之遞繫句之外，自然手語的溝通效率與語意清晰度皆高於文法手語。受試者的兩套手語系統能力均等，且兩套手語使用頻率主要決定於談話對象的語言使用。語言刻板印象與手語政策態度的調查結果顯示，受試者對自然手語有較高的評價。 依據研究結果，本論文建議現階段手語政策應調整其語言規劃方針，將自然手語納入啟聰學校正式教學語言。對未來手語政策規劃之建議為：研訂相關法令、設立專職機構、擴充手語詞彙並編撰手語字典、明訂啟聰學校教師教學溝通政策與鑑定教師手語能力、培育專業手語翻譯人才、設置手語相關節目並提供無溝通障礙環境、獎勵手語研究與推廣工作、增設相關系所。 關鍵字：台灣自然手語、中文文法手語、語言態度、語言政策 / This thesis aims to (1) compares the language structure of Chinese Signed Language (CSL) with Taiwan Sign Language (TSL), and investigates the efficiency, vagueness, and ambiguity of these two language systems; (2) to provide a preliminary evaluation of the implementation of Sign Language Policy in Taiwan through an investigation of the deaf’s proficiency in CSL and TSL, their use of them, and their attitudes toward both these two linguistic systems and the related policy. Both quantitative and qualitative analyses are adopted. Quantitative analysis includes two tests. On “structure evaluation test,” the efficiency, vagueness, and ambiguity of CSL and TSL are investigated. Evaluated items are taped into 194 segments of films, distributed on 7 linguistic levels, including lexical items, phrases, tense, adverbs, simple sentences, complex sentences, and discourse. Subjects are required to answer the questionnaire immediately after each test item is shown. “Sign language use and attitude questionnaire” is to elicit the deaf’s language proficiency, language use, and language attitudes. 75 questionnaires are collected through nonprobability sampling and nonparamentric statistical test with all the subjects being deaf adults who live in Taipei area and use sign language for communication. For qualitative analysis, 6 informants were interviewed through judgemental samplings to interpret the results of the questionnaires. The results of statistic tests indicate that TSL is more efficient, less vague and less ambiguous than CSL. Moreover, the subjects’ proficiency in the two sign language systems are equally good and their frequency of language use are decided by their interlocutors. As to their attitudes toward the two sign languages and the related language policy, all the subjects show support to TSL. Based on the findings from the quantitative and qualitative analysis, suggestions are given as follows. Legislate the law. Establish a government institution, institute lexicology, set the instructional language of the deaf school and evaluate the proficiency of deaf school teachers. Train the interpreters and provide communication unimpediment environment. Investigate sign language research, and plant institution. Key words: Taiwan Sign Language, Chinese Signed Language, language attitude, language policy

A presente dissertação analisa os índices nas quedas das matrículas iniciais nos cursos de Educação de Jovens e Adultos no Brasil entre 2000 a 2012, com ênfase a partir do ano de 2008 após a Reorganização destes cursos na cidade de São Paulo, promovida pela Secretaria Municipal de Educação. Os conceitos que fundamentaram nossas análises foram os do trabalho, educação e das contradições, analisados sob o capital. Na pesquisa ao ampliar a escala de observação,revelaram-se quedas nas matrículas em âmbito nacional. A partir da constatação nos índices dessas quedas nas matrículas em EJA, tornou-se o foco da pesquisa identificar as condicionantes e as determinantes que impulsionaram tais quedas nas matrículas destes cursos para Jovens e Adultos. Buscamos fundamentar a hipótese central ao problema apresentado sob dois parâmetros. O primeiro na investigação pela abordagem quantitativa, pela frequência dos índices apontados pelos institutos oficiais de recenseamento e estatísticas consultados e analisados sob a metodologia de análise de conteúdos, de acordo com Bardin (1977) e o segundo parâmetro qualitativamente, pela presença com que os dados emergiram no levantamento empírico em campo.O materialismo dialético foi a base epistemológica que norteou o pensamento central nas análises, orientadas em Lefebvre (1969; 2006). Dos resultados,como tendência determinante,emergiu o crescimento na oferta das carteiras de trabalho assinadas, no período de realização desta pesquisa.A pesquisa eleva à discussão sobre o pensamento liberal dominante e seus discursos, dos quais, têm sustentado algumas ações de governos municipais, estaduais ou federal em políticas educacionais para os cursos dessa modalidade de ensino. Tenta desocultar o problema apresentado na pesquisa,desde as suas bases, considerando as complexas relações sociais que se estabelecem nas sociedades atuais. / This dissertation analyzes the indexes on the falls of initial enrollment in the courses Youth and Adults in Brazil from 2000 to 2012, with emphasis from the year 2008 after the reorganization of these courses in the city of São Paulo, sponsored by the Municipal education. The conceptsthat underlie our analyzes were the work, education and contradictions, analyzed under the capital. In research to expand the scale of observation, proved declines in enrollments nation wide. From the observation of these indices declines inenrollments in adult education, has become the focus of research to identify conditions and determinants that drove these declines in enrollment in these courses for youngsters and adults. We seek to support the central hypothesis to the problem in two parameters. The first research on the quantitative approach, the frequency of the indices mentioned by official institutes census and statistics consulted and analyzed unde rthe methodology of content analysis, according to Bardin(1977) and the second parameter qualitatively by the presence in the data emerged the empirical survey in the field. Dialectical materialism was the epistemological basis that guided the central thought in the analysis, oriented Lefebvre(1969, 2006). Results as determining tendency, emerged the growth in supply of work papers signed, from this research. The research raises the discussion of liberal thought and its dominant discourses, which have sustained some actions of municipal, state or federal education policy for the courses of this type of education. Tries to uncover the problem presented in the research, since its foundation, considering the complex social relations that are established in current societies.

<p>The present thesis proposes new methods for obtaining objective and accurate diagnoses in modern healthcare. Non-invasive techniques have been used to examine or diagnose three different medical conditions, namely neuropathy among diabetics, radiotherapy induced erythema (skin redness) among breast cancer patients and diagnoses of cutaneous malignant melanoma. The techniques used were Near-InfraRed spectroscopy (NIR), Multi Frequency Bio Impedance Analysis of whole body (MFBIA-body), Laser Doppler Imaging (LDI) and Digital Colour Photography (DCP).</p><p>The neuropathy for diabetics was studied in papers I and II. The first study was performed on diabetics and control subjects of both genders. A separation was seen between males and females and therefore the data had to be divided in order to obtain good models. NIR spectroscopy was shown to be a viable technique for measuring neuropathy once the division according to gender was made. The second study on diabetics, where MFBIA-body was added to the analysis, was performed on males exclusively. Principal component analysis showed that healthy reference subjects tend to separate from diabetics. Also, diabetics with severe neuropathy separate from persons less affected.</p><p>The preliminary study presented in paper III was performed on breast cancer patients in order to investigate if NIR, LDI and DCP were able to detect radiotherapy induced erythema. The promising results in the preliminary study motivated a new and larger study. This study, presented in papers IV and V, intended to investigate the measurement techniques further but also to examine the effect that two different skin lotions, Essex and Aloe vera have on the development of erythema. The Wilcoxon signed rank sum test showed that DCP and NIR could detect erythema, which is developed during one week of radiation treatment. LDI was able to detect erythema developed during two weeks of treatment. None of the techniques could detect any differences between the two lotions regarding the development of erythema.</p><p>The use of NIR to diagnose cutaneous malignant melanoma is presented as unpublished results in this thesis. This study gave promising but inconclusive results. NIR could be of interest for future development of instrumentation for diagnosis of skin cancer.</p>

Södra Cell sells 1 900 000 ton pulp every year. Of this 490 000 tonne is sold with a contract system based on a pricing index called PIX NBSK. This index was started in 1996 and reflects the price of pulp from conferious forest. We study the NBSK PIX value of softwood from October 1996 to December 2006. People working in this branch known that there is strong periodicity in the prices. We use predictive analysis to see if clients can benefit from the periodicity and use the options in the contract system Södra offers today. We conclude that a drawback for the current contract system is that there are too many contracts in proportion to the duration time that is one year for all contracts. Using a time series model called ARMA we make successfull predictions the price difference between two contracts. Based on this prediction we change between these contracts, reducing the price with 0.81% in mean during 1997-2006. Due to the total turnover, if all clients would used such predictions during 1997-2006 Södra's income would have been reduced with 2.77 million USD a year in mean. The prices used before PIX are called list prices. The list prices seem to behave like the PIX index. Supposing that the same contract system we see in PIX today was used 1975-2006 with the list price as the base index I made a prediction of the list prices from 1986-2006. Thanks to my predictions, if I had been a client during this period and under mentioned considerations I would have been buying pulp to a price reduced with 0.57%. If clients had known the PIX between 1996-2006 in say 1995 Södra's contract system based on PIX would give them a price reduction that were 1.5% in mean during 1996-2006. Price reduction is not possible all years, but when it occurs it can be as big as 3% of the price. Suppose the clients always choose the contract with the lowest price and thereby get a reduced price over time. Then with 95% probability over a long period the price reduction is somewhere in between 0.4-2.7%. To strangle this price reduction possibility for the clients there are two ways to go: either reduce the number of contracts or extend the duration time of the contracts. To find a suitable duration time, we do spectral density estimation to get indications of which periods that are most important. From this we see that PIX index has a period of five years, wavelet approximated PIX index has 3.4 years and the list prices has a period of 5.6 years. This indicates that current duration time one year is too short. Therefore if it wouldn't effect Södra's clients, an extension of the duration time from one to five years would be good. If Södra don't extend the duration time of the contracts my recommendation is to have fewer contracts. The possibility to change between the contracts ''average last three months'' and ''average current month'' every other year is the weakest point of today's system. Therefore I recommend stop selling pulp to the contract ''average PIX last three months''. We can't prove any longterm difference between the contracts. If Södra chooses to have just one contract from this point of view it does not matter which one they choose. However, it seems like a good idea to follow the global market and therefore I recommend to choose ''average PIX current month'' rather than ''average PIX last three months'' which lags behind the market front. Since the price ''average current month'' is available at FOEX web page I think Södra should choose this contract if they decide to have only one contract. / Södra Cell säljer årligen 1 900 000 ton pappersmassa. Av denna mängd säljs 490 000 ton enligt ett kontraktsystem baserat på ett prisindex som heter PIX NBSK. Detta index introducerades 1996 och reflekterar priset på pappersmassa gjord av barrträd. Jag studerar priset på indexet från Oktober 1996 till December 2006. Dagens kontraktsystem är baserat på kontrakt med löptiden ett år. Jag undersöker om man kan prediktera prisskilllnaden mellan kontrakten, dra nytta att dagens löptid som bara är ett år och välja det kontrakt som ger det billigaste priset så ofta att priset över lång tid reduceras. När man predikterar gör man en uppskattningen av framtiden utifrån en modell av hur framtid beror på dåtid och nutid. Den modell jag har använt kallas ARMA. Denna tillsammans med priserna på pappersmassa från 1975 och framåt gav mig ett fruktbart sätt att förutsäga priserna. Resultatet blev ett pris reducerat med 0.81% i medel under perioden 1996-2006. Eftersom Södra ha så stor försäljningsvolym skulle de ha förlorat 2.27 miljoner dollar per ton i medel om alla kunder ha spekulerat utifrån den modellen jag använde. Om dagens kontraktsystem hade börjat användas 1975 med listpriserna som bas hade en kund som använt min prediktionsmetod fått ett pris reducerat med 0.57% under perioden 1986-2006. Om kunderna i förväg hade vetat priset under 1996-2001 gav det nuvarande systemet en reducerad medelintäkt med 1.5% av priset. Enskilda år reducerades intäkten med så mycket som 3%. Beräknar man konfidensintervall för prisreduktionerna så inser man att på lång sikt kommer dessa vara av storleksordningen 0.4-2.7% med sannolikheten 95%. Detta förutsatt att klienterna kan se in i framtiden. Siffran 2.7% alltså ett mått på hur stor risk man tar med dagens system. Jag tror inte att klienterna kommer reducera priset med 2.7% med nuvarande system, men det är en övre gräns. De gynsamma prediktionerna har sitt ursprung i att det finns periodicitet i priserna. Jag undersöker denna periodicitet med spektralanalys. Periodiciteten för PIX indexet är starkast kring 5 år. En wavelet-approximation av PIX-indexet hade störst periodicitet kring 3.4 år. Listpriserna hade starkast periodicitet kring 5.6 år. Detta indikerar att den nuvarande löptiden, ett år, är för kort. En lämpligare löptid för kontrakten är 5 år. Förmodligen är fem års löptid alltför lång tid att binda sig för många kunder. Därför föreslår jag att man reducerar antalet kontrakt istället. Den största svagheten i dagens system är den korta löptiden tillsammans med kontrakten ''average current month'' och ''average last three months''. Jag rekommenderar att man slutar erbjuda kontraktet ''average last three months''. Det allra säkraste är att endast erbjuda ett kontrakt. Vi har inte kunnat påvisa några skillnader över lång sikt mellan kontrakten såtillvida att något kontrakt skulle ge ett lägre medelpris än ett annat. Ur den aspekten är det godtyckligt vilket kontrakt man väljer, men det verkar vettigt att följa den globala marknaden. Därför är det eftersläpande kontraktet ''average PIX last three months'' inte att rekommendera, välj heller ''average PIX current month''. Ett annat argument för att välja ''average PIX current month'' är att dessa priser finns på FOEX hemsida och inga extra beräkningar behöver göras.

<p>Södra Cell sells 1 900 000 ton pulp every year. Of this 490 000 tonne is sold with a contract system based on a pricing index called PIX NBSK. This index was started in 1996 and reflects the price of pulp from conferious forest. We study the NBSK PIX value of softwood from October 1996 to December 2006.</p><p>People working in this branch known that there is strong periodicity in the prices. We use predictive analysis to see if clients can benefit from the periodicity and use the options in the contract system Södra offers today. We conclude that a drawback for the current contract system is that there are too many contracts in proportion to the duration time that is one year for all contracts. Using a time series model called ARMA we make successfull predictions the price difference between two contracts. Based on this prediction we change between these contracts, reducing the price with 0.81% in mean during 1997-2006. Due to the total turnover, if all clients would used such predictions during 1997-2006 Södra's income would have been reduced with 2.77 million USD a year in mean.</p><p>The prices used before PIX are called list prices. The list prices seem to behave like the PIX index. Supposing that the same contract system we see in PIX today was used 1975-2006 with the list price as the base index I made a prediction of the list prices from 1986-2006. Thanks to my predictions, if I had been a client during this period and under mentioned considerations I would have been buying pulp to a price reduced with 0.57%.</p><p>If clients had known the PIX between 1996-2006 in say 1995 Södra's contract system based on PIX would give them a price reduction that were 1.5% in mean during 1996-2006. Price reduction is not possible all years, but when it occurs it can be as big as 3% of the price. Suppose the clients always choose the contract with the lowest price and thereby get a reduced price over time. Then with 95% probability over a long period the price reduction is somewhere in between 0.4-2.7%.</p><p>To strangle this price reduction possibility for the clients there are two ways to go: either reduce the number of contracts or extend the duration time of the contracts.</p><p>To find a suitable duration time, we do spectral density estimation to get indications of which periods that are most important. From this we see that PIX index has a period of five years, wavelet approximated PIX index has 3.4 years and the list prices has a period of 5.6 years. This indicates that current duration time one year is too short. Therefore if it wouldn't effect Södra's clients, an extension of the duration time from one to five years would be good.</p><p>If Södra don't extend the duration time of the contracts my recommendation is to have fewer contracts. The possibility to change between the contracts ''average last three months'' and ''average current month'' every other year is the weakest point of today's system. Therefore I recommend stop selling pulp to the contract ''average PIX last three months''.</p><p>We can't prove any longterm difference between the contracts. If Södra chooses to have just one contract from this point of view it does not matter which one they choose. However, it seems like a good idea to follow the global market and therefore I recommend to choose ''average PIX current month'' rather than ''average PIX last three months'' which lags behind the market front. Since the price ''average current month'' is available at FOEX web page I think Södra should choose this contract if they decide to have only one contract.</p> / <p>Södra Cell säljer årligen 1 900 000 ton pappersmassa. Av denna mängd säljs 490 000 ton enligt ett kontraktsystem baserat på ett prisindex som heter PIX NBSK. Detta index introducerades 1996 och reflekterar priset på pappersmassa gjord av barrträd. Jag studerar priset på indexet från Oktober 1996 till December 2006.</p><p>Dagens kontraktsystem är baserat på kontrakt med löptiden ett år. Jag undersöker om man kan prediktera prisskilllnaden mellan kontrakten, dra nytta att dagens löptid som bara är ett år och välja det kontrakt som ger det billigaste priset så ofta att priset över lång tid reduceras. När man predikterar gör man en uppskattningen av framtiden utifrån en modell av hur framtid beror på dåtid och nutid. Den modell jag har använt kallas ARMA. Denna tillsammans med priserna på pappersmassa från 1975 och framåt gav mig ett fruktbart sätt att förutsäga priserna. Resultatet blev ett pris reducerat med 0.81% i medel under perioden 1996-2006. Eftersom Södra ha så stor försäljningsvolym skulle de ha förlorat 2.27 miljoner dollar per ton i medel om alla kunder ha spekulerat utifrån den modellen jag använde.</p><p>Om dagens kontraktsystem hade börjat användas 1975 med listpriserna som bas hade en kund som använt min prediktionsmetod fått ett pris reducerat med 0.57% under perioden 1986-2006.</p><p>Om kunderna i förväg hade vetat priset under 1996-2001 gav det nuvarande systemet en reducerad medelintäkt med 1.5% av priset. Enskilda år reducerades intäkten med så mycket som 3%. Beräknar man konfidensintervall för prisreduktionerna så inser man att på lång sikt kommer dessa vara av storleksordningen 0.4-2.7% med sannolikheten 95%. Detta förutsatt att klienterna kan se in i framtiden. Siffran 2.7% alltså ett mått på hur stor risk man tar med dagens system. Jag tror inte att klienterna kommer reducera priset med 2.7% med nuvarande system, men det är en övre gräns.</p><p>De gynsamma prediktionerna har sitt ursprung i att det finns periodicitet i priserna. Jag undersöker denna periodicitet med spektralanalys. Periodiciteten för PIX indexet är starkast kring 5 år. En wavelet-approximation av PIX-indexet hade störst periodicitet kring 3.4 år. Listpriserna hade starkast periodicitet kring 5.6 år. Detta indikerar att den nuvarande löptiden, ett år, är för kort. En lämpligare löptid för kontrakten är 5 år.</p><p>Förmodligen är fem års löptid alltför lång tid att binda sig för många kunder. Därför föreslår jag att man reducerar antalet kontrakt istället. Den största svagheten i dagens system är den korta löptiden tillsammans med kontrakten ''average current month'' och ''average last three months''. Jag rekommenderar att man slutar erbjuda kontraktet ''average last three months''. Det allra säkraste är att endast erbjuda ett kontrakt. Vi har inte kunnat påvisa några skillnader över lång sikt mellan kontrakten såtillvida att något kontrakt skulle ge ett lägre medelpris än ett annat. Ur den aspekten är det godtyckligt vilket kontrakt man väljer, men det verkar vettigt att följa den globala marknaden. Därför är det eftersläpande kontraktet ''average PIX last three months'' inte att rekommendera, välj heller ''average PIX current month''. Ett annat argument för att välja ''average PIX current month'' är att dessa priser finns på FOEX hemsida och inga extra beräkningar behöver göras.</p>

The main contribution of this thesis is the implementation of manufacturing constraints in shape and topology optimization. Fabrication limitations related to the casting process are formulated as mathematical constraints and introduced in the optimization algorithm. In addition, based on the same theoretical and modelization tools, we propose a novel formulation for multi-phase optimization problems, which can be extended to the optimization of structures with functionally-graded properties. A key ingredient for the mathematical formulation of most problems throughout our work is the notion of the signed distance function to a domain. This work is divided into three parts. The rst part is bibliographical and contains the necessary background material for the understanding of the thesis' main core. It includes the rst two chapters. Chapter 1 provides a synopsis of shape and topology optimization methods and emphasizes the combination of shape sensitivity analysis and the level-set method for tracking a shape's boundary. In Chapter 2 we give a short description of the casting process, from which all our manufacturing constraints derive. We explain how industrial designers account for these limitations and propose a strategy to incorporate them in shape and topology optimization algorithms. The second part is about the mathematical formulation of manufacturing constraints. It starts with Chapter 3, where the control of thickness is discussed. Based on the signed distance function, we formulate three constraints to ensure a maximum and minimm feature size, as well as a minimal distance between structural members. Then, in Chapter 4, we propose ways to handle molding direction constraints and combine them with thickness constraints. Finally, a thermal constraint coming from the solidi cation of cast parts is treated in Chapter 5 using several thermal models. Multi-phase optimization is discussed in the third part. The general problem of shape and topology optimization using multiple phases is presented in detail in Chapter 6. A "smoothed-interface" approach, based again on the signed distance function, is proposed to avoid numerical di culties related to classical "sharp-interface" problems and a shape derivative is calculated. An extension of this novel formulation to general types of material properties' gradation is shown in the Appendix A.